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Wave Energy Converters (WECs) with optimised geometries and control systems have been developed in recent years to advance marine energy technologies towards commercialisation. In particular, a number of WEC hull geometry optimisation studies have been performed, due to the high cost reduction potential associated with the device structure. However, no standard and consistent method has been established for this purpose. For example, different optimisation formulations (single-objective and multi-objective), have been used, applying different optimisation algorithms. Additionally, a range of objective functions have been employed, where power maximisation has been represented through a variety of metrics, and cost minimisation expressed with diverse cost proxies. The goal of this study is to address the challenge of finding a suitable optimisation problem formulation with single-objective or multi-objective implementations, and the respective objective functions, that support the exploration of shapes that reduce the levelised cost of energy. Results show that submerged surface area cost proxies are more suitable for this purpose than volume-based cost proxies. Results from a multi-objective optimisation formulation can provide a good understanding of the solution space, whereas results from single-objective studies can be used for seeding these multi-objective optimisation approaches. • Different objective functions are compared for wave energy converter optimisation. • Using volume based cost proxies results in more complex WEC shapes. • From a techno-economic perspective surface area based cost proxies are more suitable. • Multi-objective implementations are studied and compared to single-objective approaches. • Single-objective results should be used as inputs to multi-objective formulations. [ABSTRACT FROM AUTHOR]